In Tucson itself the shops I like the most are: The Quilt Basket, Quilt Market, and Bella's.
Gads, but there are a few others on the way to Tucson. One is a double wide trailer out in the country that has so much fabric you almost get lost and then wonder how that lady got so much fabric in that space. Maybe someone else on the BQ knows the name and location.
Up here Phoenix way there is 35th Avenue Sew & Vac, which is supposed to have the larges inventory in the state. It's Fabric World is carefully hidden and you might want to ask how to get to it as it is down a bit of a ramp past all the sewing machines.
From 35th Ave S&V if you go west there is The Cactus Bee 75th Ave and W. Cactus. On up toward Sun City there is Arizona Quilts at 99th Ave & Beardsley and then Sun Valley Quilts @ 9857 W. Bell Rd just inside Sun City. Unfortunately the quilt store in Surprise closed.
In the West Valley there is Bearly Stitchin and In Stitches, both in Goodyear.
Have fun.
ali